The purpose of this study is to assess the safety and efficacy of avelumab in patients with metastatic neuroendocrine-like prostate cancer. Eligible men will be started on avelumab every 2 weeks and will stay on therapy until progression or intolerable side effects. The central hypothesis is that PD-L1 inhibition with avelumab will be efficacious based on radiographic responses in a subset of men with metastatic neuroendocrine-like prostate cancer and be reasonably well tolerated, meeting criteria for further study in larger phase 2 and 3 trials based on meeting pre-specified efficacy rates and prolonged PFS in some men.

Inclusion Criteria:

1. Neuroendocrine-like prostate cancer, based on histology OR based on clinical presentation as defined by meeting one of the two below criteria. All subjects must submit their primary tumor or metastatic biopsy pathology specimens to the Duke Cancer Institute where they will be centrally reviewed by Duke Pathology. Central Duke pathologic review is not required for screening but rather for confirmation of histologic subtype. Local pathologic review is sufficient for eligibility determination.

   1. Criterion 1: Presence of 1 of 3 histologically proven diagnoses: 1) Primary small cell carcinoma of the prostate, defined by classic histologic features such as small tumor cells with scanty cytoplasm, darkly stained nuclei with homogeneous chromatin pattern. The tumor cells do not form glandular structure but grow as solid sheets with frequent mitotic figures and necrosis; 2) Intermediate atypical carcinoma of the prostate, which has histologic features distinct from small cell carcinoma or adenocarcinoma. The tumor grows as solid sheets or vague glandular structures. The tumor cells have moderate amounts of cytoplasm and centrally located, round and regular nuclei with fine, granular and homogeneous chromatin. Mitosis and necrosis are absent; 3) mixed histology tumors of the prostate, containing both adenocarcinoma and neuroendocrine or small cell components.
   2. Criterion 2: Presence of histologically proven adenocarcinoma of the prostate without any sign of neuroendocrine or small cell histology that is radiographically progressing despite castrate levels of testosterone (<50 ng/mL) with the following poor risk features:

   i. Prior progression despite therapy with either abiraterone acetate and/or enzalutamide ii. At least one of the following: 1) Liver metastases; 2) Bulky radiographic progression (≥2 cm short axis lymph nodes or ≥1 cm long axis visceral metastases) combined with low serum PSA (<10ng/mL); 3) High serum LDH (>1X upper limit of normal).

2. Measurable disease as defined by modified PCWG3 using iRECIST criteria

3. Available tumor tissue for pathologic review and correlative studies. Tumor tissue (localized or metastatic) does not need to be received but rather identified and available (slides and/or blocks) to be sent to Duke.

4. Documented progressive metastatic CRPC based on at least one of the following criteria:

   1. PSA progression defined as 25% increase over baseline value with an increase in the absolute value of at least 2.0 ng/mL that is confirmed by another PSA level with a minimum of a 1 week interval and a minimum PSA of 2.0 ng/mL. Note: If confirmed rise is the only indication of progression, a minimal starting value of 1.0 ng/mL is acceptable, unless pure small-cell carcinoma.
   2. Soft-tissue progression based on new lesions or growth of existing soft tissue metastases.
   3. Progression of bone disease (evaluable disease) or (new bone lesion(s)) by bone scan.

5. Castrate levels of serum total testosterone (<50 ng/dl) OR ongoing documented ADT unless pure small cell prostate cancer is present.

6. Previous use of radiation to metastatic site(s) at any time prior to enrollment is allowed, provided that this site is not the only measurable disease present or unless that solitary site is progressing following radiation.

7. Patients should have received at least one line of approved chemotherapy and/or hormonal therapy

8. Previous cytotoxic chemotherapy including cisplatin, carboplatin, oxaliplatin, etoposide, docetaxel, cabazitaxel, and gemcitabine is allowed, up to 3 prior regimens.

9. Karnofsky performance status of 70 or higher.

10. Acceptable initial laboratory values within 14 days of Cycle 1 Day 1 according to the below table:

    ANC ≥ 1500/µl Hemoglobin ≥ 9.0 g/dL(prior transfusion permitted) Platelet count ≥ 100,000/µl Creatinine ≤ 2.0 x the institutional upper limit of normal (ULN) OR creatinine clearance >30 ml/min Potassium ≥ 3.5 mmol/L (within institutional normal range) Bilirubin ≤ 1.5 x ULN (unless documented Gilbert's disease) SGOT (AST) ≤ 2.5x ULN, or <5x ULN in patients with documented liver metastases SGPT (ALT) ≤ 2.5x ULN or <5x ULN in patients with documented liver metastases

11. Age >18

12. Highly effective contraception for male subjects with childbearing potential throughout the study and for at least 60 days after last avelumab treatment administration if the risk of conception exists.

13. Willing and able to provide written informed consent and HIPAA authorization for the release of personal health information.

14. Life expectancy of over 3 months as determined by treating physician.

Exclusion Criteria:

1. Prior usage of PD-1 inhibitors, programed-death ligand 1 and/or 2 inhibitors, CTLA-4 inhibitors including but not limited to ipilimumab, nivolumab, avelumab, durvalumab, tremelimumab, and pembrolizumab.
2. Active on-going immunologic or autoimmune disease including but not limited to systemic or cutaneous lupus erythematosus, cutaneous psoriasis, psoriatic arthritis, rheumatoid arthritis, scleroderma, sicca syndrome, polymyalgia rheumatica, polyarteritis nodosa, granulomatous polyangiitis, microscopic polyangiitis, polyarteritis nodosa, temporal arteritis, giant cell arteritis, dermatomyositis, Kawasaki disease.
3. Previous malignancy within 3 years other than non-melanomatous skin cancers or cancers of low malignant potential such as non-invasive urothelial carcinoma.
4. Any other on-going chemotherapeutic, biologic, radiopharmaceutical, or investigational agent currently or within 28 days of Cycle 1 Day 1.
5. Prior use of abiraterone and other hormonal agents used to treat prostate cancer are permitted but abiraterone acetate should be stopped prior to study treatment initiation.
6. Current usage of immunosuppressant medication except for a) intranasal, inhaled, and topical corticosteroids and b) systemic corticosteroids equivalent to ≤ 10 mg/day of prednisone, c) steroids as premedication for hypersensitivity reactions (e.g. CT scan premedication).
7. Prior organ transplantation including allogeneic stem-cell transplants.
8. Active bacterial or viral infections requiring systemic therapy.
9. Current active infections with HIV/AIDS, Hepatitis B, and Hepatitis C requiring treatment.
10. Live virus vaccination within 4 weeks of the first dose of avelumab (inactivated vaccines are allowed).
11. Known prior hypersensitivity to the investigational product or any component formulations, including known severe hypersensitivity reactions to monoclonal antibodies.
12. Clinically significant (i.e. active) cardiovascular disease: cerebral vascular accident (<6 months prior to enrollment), myocardial infarction (<6 months prior to enrollment), unstable angina, congestive heart failure (≥ New York Heart Association Classification Class II), or serious cardiac arrhythmia requiring medication.
13. Persisting toxicity related to prior therapy (NCI CTCAE v. 4.03 Grade > 1); however, alopecia, sensory neuropathy Grade ≤ 2, Grade 2 anemia, or other Grade ≤ 2 not constituting a safety risk based on investigator's judgment are acceptable.
14. Other severe acute or chronic medical conditions including colitis, inflammatory bowel disease, pneumonitis, pulmonary fibrosis or psychiatric conditions including recent (within the past year) or active suicidal ideation or behavior; or laboratory abnormalities that may increase the risk associated with study participation or study treatment administration or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the patient inappropriate for entry into this study.

Up to 30 days post last day of dosing